On the structure of manifolds with positive scalar curvature

Richard Schoen Shing-Tung Yau

Differential Geometry mathscidoc:1912.43466

Manuscripta mathematica, 28, (1), 159-183, 1979.1
In this paper, we study the question of which compact manifolds admit a metric with positive scalar curvature. Scalar curvature is perhaps the weakest invariant among all the well-known invariants constructed from the curvature tensor. It measures the deviation of the Riemannian volume of the geodesic ball from the euclidean volume of the geodesic ball. As a result, it does not tell us much of the behavior of the geodesics in the manifold. Therefore it was remarkable that in 1963, Lichnerowicz [i] was able to prove the theorem that on a compact spin manifold with positive scalar curvature, there is no harmonic spinor. Applying
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  title={On the structure of manifolds with positive scalar curvature},
  author={Richard Schoen, and Shing-Tung Yau},
  booktitle={Manuscripta mathematica},
Richard Schoen, and Shing-Tung Yau. On the structure of manifolds with positive scalar curvature. 1979. Vol. 28. In Manuscripta mathematica. pp.159-183. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224203436273646030.
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